Publication

MAP Estimation for Bayesian Mixture Models with Submodular Priors

Volkan Cevher, Luca Baldassarre, Marwa El Halabi
2014
Conference Papers

Abstract

We propose a Bayesian approach where the signal structure can be represented by a mixture model with a submodular prior. We consider an observation model that leads to Lipschitz functions. Due to its combinatorial nature, computing the maximum a posteriori estimate for this model is NP-Hard, nonetheless our converging majorization-minimization scheme yields approximate estimates that, in practice, outperform state-of-the-art methods.

Official source

https://infoscience.epfl.ch/entities/publication/e70ad2c1-085f-4ef3-9c98-1fed7b8f916f

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Volkan Cevher, Luca Baldassarre, Marwa El Halabi
2014
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e70ad2c1-085f-4ef3-9c98-1fed7b8f916f

About this result

Related concepts (20)

Maximum a posteriori estimation

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

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